“It is really serious now,” said Greg Doran, the artistic director of the RSC. “And if we lose our performance culture, we lose it for good.” The leaders of the theatres also warn that while they struggle to stay afloat, the whole performing arts sector is in “huge jeopardy”, and that without swift action there will be little left for audiences to see across the country when restrictions are lifted.

Rufus Norris, the artistic director of the NT, said the government should recognise that continued social distancing means most theatres are no longer viable businesses.

In an interview with Sunday’s Observer, he reveals that waiting until next year to open “would involve us going insolvent”. He added: “Without additional government support 70% of theatres will be boarded up by Christmas.”

The NT, he said, is losing between £4m and £5m a month in lockdown.

At Stratford-upon-Avon, Doran said the RSC has lost 95% of its trading income. “We urgently need an immediate extension to the tax relief scheme and more guidance on the rules for mass gatherings. But we can’t just save the national flagships and then assume we are going to be all right. We rely on the talent trained across the nation.”

The three venues will not survive into 2021 without healthy box-office takings and are suffering the same pain crippling regional theatres, but on a larger scale. This week they have drawn up an urgent appeal to the parliamentary committee on digital, culture, media and sport, seen by the Observer, in which they ask for four emergency moves to pull them back from the brink. They want a major cash injection or loan to aid recovery, further help for freelancers, a boost to the existing theatre tax credit scheme, and an extension of the job retention scheme.

Lisa Burger, the executive director of the NT, defended the proposed redundancies this weekend, saying she needs to reduce staff costs by 20% to 30% if the venue is to have a future. “It was a decision taken by the board and the executive. There should be no suspicion we are ‘crying wolf’,” she said. The company’s vulnerability, she added, is partly due to its success at finding funds from outside government subsidy in the past: “It is a sad kind of punishment for all the work we have done developing new income streams.”

At Covent Garden, home of the Royal Opera and the Royal Ballet companies, the chief executive, Alex Beard, has seen 60% of house income fall away. “We are not just a cultural symbol, we are the single largest employer of artists in the country, other than the BBC. Our level of subsidy is less than 20%, compared to around 70 per cent at opera houses in Europe, and our box office needs 95% occupancy to break even,” he said. “As organisations we are the antithesis of social distancing and I think the government now understands the gravity of the situation. You just have to imagine London without the West End, or Leeds without Opera North.”

The National Theatre says it needs to reduce staff costs by nearly a third.Photograph: Alamy

The NT, ROH and RSC are searching for ways to reopen on a smaller scale, but each needs hefty box-office receipts just to run their large buildings. In the interim they are streaming work online. More than eight million watched the NT’s One Man, Two Guvnors, and a production of Tennessee Williams’ A Streetcar Named Desire is on show now.

Writing in the Observer, the culture secretary Oliver Dowden said he was “clear-eyed” about the “huge challenges” faced by theatres. “I know the pandemic has dealt the arts a knock-out blow,” he writes. “Live theatre has been particularly hard hit and faces some of the biggest obstacles to its return.” Last week he created a cultural renewal taskforce, headed by Neil Mendoza, to look at crisis measures for the sector.

“It is great if the government recognises this moment of huge jeopardy,” said Beard. “After all, it was the same great impulse behind setting up both the NHS and the ROH after the war: a concern for the nation’s physical and cultural wellbeing. And we rely on a pipeline of specialist talent coming from across the sector.”

Beard also welcomes the collegiate effort going on across the performance industry. The theatre impresario Sonia Friedman is one of those attempting to prevent widespread collapse and shewarned last week that more than 1,000 theatres around the country were in danger of closure. The Old Vic and the Royal Albert Hall have issued recent distress calls, while the Royal Lyceum in Edinburgh has shut down and the Nuffield in Southampton has gone into administration.

“If this goes on much longer, it’s hard to imagine any theatre surviving,” Norris said. “Whatever it means for the National, you can multiply for regional theatres.”

Doran regards the RSC as “the national theatre of the regions” and said he owes his work as a director to seeing performances at the Bolton Octagon and the Everyman in Liverpool as a young man. “I started my career in Nottingham and in then in York. This is a fragile infrastructure and the RSC needs to survive to help those theatres.”

Adam Penford, artistic director of the Nottingham Playhouse, said he fears for the country’s cultural chances: “Theatre in the UK is based on interdependent relationships. Take one part out and the whole thing collapses.”

Doran said when the country’s Covid-19 death figures reached 33,000 this month, the same number who died in the plague that shut theatres in 1603, he realised that British culture would change for ever, as it did in Shakespeare’s era. “As a playwright his whole world view changed. It makes me wish we could go back to last year, or as his Richard II says, ‘Call back yesterday, bid time return’.”